The question provides contradictory information for a single circle (if radius is 8 cm, diameter should be 16 cm; if diameter is 10 mm, radius should be 5 mm).

$$
C = 16\pi \text{ cm}
$$
$$
C \approx 16 \times 3.14159 \text{ cm}
$$
$$
C \approx 50.27 \text{ cm}
$$
The circumference is $\boxed{16\pi \text{ cm}}$ or approximately $\boxed{50.27 \text{ cm}}$.

• Scenario 2: Using diameter $d = 10 \text{ mm}$

$$
C = \pi \text{ cm}
$$
$$
C \approx 3.14159 \text{ cm}
$$
$$
C \approx 3.14 \text{ cm}
$$
The circumference is $\boxed{\pi \text{ cm}}$ or approximately $\boxed{3.14 \text{ cm}}$.

4. Calculate the volume of a cylinder with base $25 \text{ cm}^2$ and height $20 \text{ cm}$.

The volume of the cylinder is $\boxed{500 \text{ cm}^3}$.

5. Calculate the mode, median and mean of $133, 138, 124, 129, 133, 127, 138, 136$.

There are $n=8$ data points.

The mode is the value that appears most frequently. In this set, 133 appears twice and 138 appears twice.
The mode is $\boxed{133 \text{ and } 138}$.

Since there is an even number of data points ($n=8$), the median is the average of the two middle values (the 4th and 5th values).
The 4th value is 133.
The 5th value is 133.

The median is $\boxed{133}$.

The mean is the sum of all values divided by the number of values.

The mean is $\boxed{132.25}$.